LEARN · EXPLAIN · REVISE

Which pair gives all the roots?

Read the idea, work independently, then explain what changed.

TOPIC 01

Quadratic equations and functions

Their sum is 7/2 and product is 3/2, agreeing with −b/a and c/a. Both values also give zero on substitution.

PREDICT → MOVE → EXPLAIN

Before moving a slider, predict the opening, vertex and intercepts. Then compare the graph with your prediction.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

2x^2-7x+3=0

Working and explanation

BUILD THE REASONING

Hint 1

Look for two factors whose product is 2x² − 7x + 3.

Hint 2

Try factors with first terms 2x and x, and constants −1 and −3.

Worked solution

Factor the quadratic.
$2x^2-7x+3=(2x-1)(x-3)$
A product is zero when at least one factor is zero.
$2x-1=0\ \text{or}\ x-3=0\Rightarrow x=\tfrac12\ \text{or}\ 3$

C: the roots are 1/2 and 3.

Checks and common pitfalls: Their sum is 7/2 and product is 3/2, agreeing with −b/a and c/a. Both values also give zero on substitution.

Think first. Reveal a hint when the class is ready.